Chapter 14.1, Problem 78E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Comparing Different Orders of Integration Using Technology In Exercises 77 and 78, (a) sketch the region of integration, (b) change the order of integration, and (c) use a computer algebra system to show that both orders yield the same value. ∫ 0 2 ∫ 4 − x 2 4 − ( x 2 / 4 ) x y x 2 + y 2 + 1   d y   d x

(a)

To determine

To graph: The region of integration for the given expression.

Explanation

Given:

The expression âˆ«02âˆ«4âˆ’x24âˆ’x24(xyx2+y2+1)dydx.

Graph:

Take the equations y=4âˆ’x2,y=4âˆ’x24,x=0,x=2 into consideration. In order to find and draw the graph of functions, the following Ti-83 steps are used:

Step 1

(b)

To determine
The change in the order of integration

(c)

To determine

To prove: Both orders give the same value using CAS.

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